. Starter Activity To be Added Objectives Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way) For example: 1.I think of a number, subtract 7 and the answer is 16. What is my number? 2.A stack of 50 sheets of card is 12 cm high. How thick is one sheet of card? 3.In this diagram, the number in each cell is formed by adding the two numbers above it.
5
8
7
13
15
28
31
?
45
?
?
182
31
n
45
n + 31
n + 45
182
What if the top three numbers are swapped around? What if you start with four numbers? 4.I think of a number, multiply it by 6 and add 1. The answer is 37. What is my number? 5.There are 26 biscuits altogether on two plates. The second plate has 8 fewer biscuits than the first plate. How many biscuits are there on each plate? 6.Find the angle a in a triangle with angles a, a + 10, a + 20. 7.Solve these equations: a. a + 5 = 12 c. 7h – 3 = 20 e. 2c + 3 = 19 b. 3m = 18 d. 7 = 5 + 2z f. 6 = 2p – 8 8.There are 376 stones in three piles. The second pile has 24 more stones than the first pile. The third pile has twice as many stones as the second. How many stones are there in each pile? 9.On Dwain’s next birthday, half of his age will be 16. How old is Dwain now? 10.Solve these equations: a. 2.4z + 5.9 = 14.3 b. 5z – 7 = 13 – 3z c. 4(b – 1) + 5(b + 1) = 100 Extension ASolve these equations exactly. a. 7(s + 3) = 45 – 3(12 – s) b. 3(2a – 1) = 5(4a – 1) – 4(3a – 2) c. 2(m – 0.3) – 3(m – 1.3) = 4(3m + 3.1) d. 3⁄4(c – 1) = 1⁄2(5c – 3) e. x – 3 = x – 2 2 3 Solve these equations exactly. Each has two solutions. a. + 24 = 60 b. 3 = 11.Begin to use graphs and set up equations to solve simple problems involving direct proportion. Discuss practical examples of direct proportion, such as: • the number of euros you can buy for any amount in pounds sterling (no commission fee); • the number of kilometres equal to a given number of miles, assuming 8 km to every 5 miles; • the cost of tennis balls, originally at ￡3 each, offered at ￡2 each in a sale. For example, generate sets of proportional pairs by multiplying and test successive ratios to see if they are equal: Check by drawing a graph, using pencil and paper or ICT. Plenary
Starter Activity
To be Added
Objectives
Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way)
For example:
1. I think of a number, subtract 7 and the answer is 16.
What is my number?
2. A stack of 50 sheets of card is 12 cm high.
How thick is one sheet of card?
3. In this diagram, the number in each
cell is formed by adding the two
numbers above it.
What if the top three numbers are swapped around?
What if you start with four numbers?
4. I think of a number, multiply it by 6 and add 1.
The answer is 37. What is my number?
5. There are 26 biscuits altogether on two plates.
The second plate has 8 fewer biscuits than the first plate.
How many biscuits are there on each plate?
6. Find the angle a in a triangle with angles a, a + 10, a + 20.
7. Solve these equations:
a. a + 5 = 12 c. 7h – 3 = 20 e. 2c + 3 = 19
b. 3m = 18 d. 7 = 5 + 2z f. 6 = 2p – 8
8. There are 376 stones in three piles. The second pile
has 24 more stones than the first pile. The third pile
has twice as many stones as the second.
How many stones are there in each pile?
9. On Dwain’s next birthday, half of his age will
be 16. How old is Dwain now?
10. Solve these equations:
a. 2.4z + 5.9 = 14.3
b. 5z – 7 = 13 – 3z
c. 4(b – 1) + 5(b + 1) = 100
Extension
A Solve these equations exactly.
a. 7(s + 3) = 45 – 3(12 – s)
b. 3(2a – 1) = 5(4a – 1) – 4(3a – 2)
c. 2(m – 0.3) – 3(m – 1.3) = 4(3m + 3.1)
d. 3⁄4(c – 1) = 1⁄2(5c – 3)
e. x – 3 = x – 2
2 3
Solve these equations exactly.
Each has two solutions.
a. + 24 = 60
b. 3 =
11. Begin to use graphs and set up equations to solve
simple problems involving direct proportion.
Discuss practical examples of direct proportion,
such as:
• the number of euros you can buy for any amount in
pounds sterling (no commission fee);
• the number of kilometres equal to a given number
of miles, assuming 8 km to every 5 miles;
• the cost of tennis balls, originally at ￡3 each, offered
at ￡2 each in a sale. For example, generate sets of
proportional pairs by multiplying and test successive
ratios to see if they are equal:
Check by drawing a graph, using pencil and paper or
ICT.
Plenary